High-multiplicity bin packing

Okay kiddo, let me help you understand high-multiplicity bin packing. You know how sometimes you need to pack your toys or other things into a box or a bag for storage or traveling? Well, bin packing is similar, but instead of toys or clothes, we use numbers or items that need to be stored or processed.

Now, high-multiplicity means we have a lot of the same type of item to pack. For example, imagine you have ten blue marbles that need to be put in a box. That's a high-multiplicity situation.

Bin packing also has a rule that says we can't waste space. So we want to put as many items as we can in each box, so we don't waste any space or any more boxes than we need to.

The challenge with high-multiplicity bin packing is that if we just put all the blue marbles, one by one, in a box, we might be wasting a lot of space. And we don't want to do that.

So what we do is try to group the marbles together so that they fit more efficiently in each box. Think of it like fitting puzzle pieces together.

For example, let's say we group three blue marbles together, and they fit in the box perfectly. We can then take another three blue marbles, and they also fit perfectly in the same box. And then we can take the remaining four blue marbles and put them in another box.

By grouping the marbles and fitting them into boxes more efficiently, we save space and reduce the number of boxes we need. This is what high-multiplicity bin packing is all about – trying to pack as many items as possible into as few boxes as possible.

I hope that makes sense, kiddo!